Weird...the screen on the S6 is the best I've ever seen, bar none. Your pic is interesting. Haven't compared it directly to the M8 but I can't imagine that difference in person. I've compared it to a number of other phones with outstanding screens and the S6 just blows them away.
I read an article that manual max brightness on the S6 is far dimmer than auto-brightness max (for some weird reason). I think max manual brightness was around 475 nits but auto was almost 750 nits so try setting it to auto and see what happens.